The private school chain run by Sir Chris Woodhead, a former chief inspector of schools, is under investigation by the Department for Education over claims that it has defrauded the generous state-run pension scheme for teachers.

Officials are acting on information from a former senior executive at Cognita, which has a multimillion-pound turnover and manages more than 50 fee-paying schools across the country.

It is claimed that, in order to lure high-achieving staff, Cognita filed paperwork to ensure that headteachers at schools not eligible to benefit from the Teachers Pensions Scheme (TPS) were registered as working in schools that are covered.

Documents seen by the Observer show that at least one headteacher, John Price, working at Chilton Cantelo, in Dorset, a school where staff are ineligible to membership of TPS, did enjoy the benefits, although the company says the arrangement is legitimate.

The matter has been internally investigated by the company’s lawyers and its chief executive, Rees Withers, wrote to the whistleblower denying there was any issue, adding that there were no grounds to accuse Cognita of dishonesty. He wrote: “Given the complexities of pension legislation it would be perfectly feasible for illegitimate arrangements to be put in place through a misunderstanding of the rules.”

However the allegation is now, according to a letter from the education secretary Michael Gove to the whistleblower’s MP, “being investigated by my officials”.

The inquiry comes at a sensitive juncture for Woodhead, whose company is said to be seeking new financial backing to fund its expansion in Asia.

It also follows revelations by the Observer last year that parents at its £7,400-a-term Southbank International school in London believed the company had been “milking profits” at the expense of children’s education.

In other allegations made to both the DfE and theObserver, the whistleblower, a former senior education officer at the firm who was sacked last summer after making the claims internally, says he was asked to take part in commercial espionage, said to be referred to as “secret shopping” within the firm.

He claims he was asked to pretend to be a prospective parent along with a female colleague in order to pick up commercially valuable information from a rival school.

He says the company’s UK marketing director, Nicole Louis, even handed him a script to use during a planned visit to St Michael’s school in Llanelli last year, which competes with Cognita’s Ffynone House school in Swansea. Ffynone House has since been transferred back to its previous charitable owners amid questions over the school’s financial viability.

Two months before he was fired, the whistleblower received a letter from Withers, saying: “I appreciate that you felt it wrong of Nicole Louis to ask you to adopt a false name and pretend to be a prospective parent and that you believe that, as a general rule, it is inappropriate for a senior employee of Cognita to adopt such an approach to assess the facilities of a rival.

“However the issue that you raised in your original letter of complaint was that such conduct constituted ‘fraudulent conduct’.

“I am satisfied that such conduct is not ‘fraudulent’ in the sense of some criminal law offence having been committed.

“I note your opinion on what the head of the school could have done. However, the point is that he did not call the police and, having already said in previous correspondence that the practice has been discontinued until the matter can be debated at board level to determine whether such an approach is ethically and commercially right for the business, I fail to see what further you expect of me.”

The whistleblower further claims there was a brutal culture at the firm. Minutes of a meeting between Woodhead, who is the firm’s chairman, and Cognita heads on 12 May 2011 records Woodhead saying:“Certain members of staff at head office should stop behaving in a brutal and cavalier fashion.”

An email, seen by the Observer, from David Baldwin, then a senior education officer at the firm, to the whistleblower in October 2010, also admits: “We cannot lose people like yourself in this often faceless, sometimes brutish company.”

Woodhead said Cognita would “robustly” defend itself but would offer no further comment. The DfE said it was aware of the allegation but could not comment further.